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Search: id:A060354
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| A060354 |
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The n-th n-gonal number. |
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+0
10
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| 0, 1, 2, 6, 16, 35, 66, 112, 176, 261, 370, 506, 672, 871, 1106, 1380, 1696, 2057, 2466, 2926, 3440, 4011, 4642, 5336, 6096, 6925, 7826, 8802, 9856, 10991, 12210, 13516, 14912, 16401, 17986, 19670, 21456, 23347, 25346, 27456, 29680, 32021
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of (0,1,0,3,0,0,0,....). - Paul Barry (pbarry(AT)wit.ie), Sep 14 2006
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
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a(n) = (n(n-2)^2+n^2)/2
E.g.f.: exp(x)*x*(1+x^2/2); - Paul Barry (pbarry(AT)wit.ie), Sep 14 2006
sum((binomial(0,0*j)+binomial(n,2)),j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 04 2006
G.f.: x(1-2x+4x^2)/(1-x)^4. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2008]
G.f.: exp(x)*(x+x^3/2) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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MAPLE
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restart: G(x):=exp(x)*(x+x^3/2): f[0]:=G(x): for n from 1 to 45 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..41); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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PROGRAM
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(PARI) { for (n=0, 1000, write("b060354.txt", n, " ", (n*(n - 2)^2 + n^2)/2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 04 2009]
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CROSSREFS
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First differences of A004255.
Sequence in context: A071522 A005996 A032091 this_sequence A140131 A159938 A145126
Adjacent sequences: A060351 A060352 A060353 this_sequence A060355 A060356 A060357
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Hareendra Yalamanchili (hyalaman(AT)mit.edu), Apr 01 2001
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